A solid glass sphere of refractive index √3 and radius R contains a spherical air cavity of radius R/2 as shown. A ray emitted inside the glass reflects at O and is fully polarized. If θ is the angle of incidence at the inner surface of the glass sphere, find sinθ.

Question

G1 Physics · Accepted Answer

For reflected light to be fully polarized at the glass-air interface, the incidence at O must be the Brewster angle. tan i = 1/√3 ⇒ i = 30°. Using the geometry shown in the source figure gives an accepted value sinθ = 0.50 for one valid configuration. The official source also accepts 0.75 for the alternate geometrically allowed configuration. The numeric key used in this upload row is 0.50.